This idea was inspired by this problem. Although it does not allow people to travel for free, it could potentially be a much cheaper alternative to conventional travel as well as allowing participants to experience travel in a brand new way.
Basically, it gives two individuals, or perhaps even two families, the opportunity to travel somewhere with no accommodation costs. In exchange, they provide the same opportunity for another family. The concept is simple enough, the idea is focused more on the company that would liaison such exchanges as a service.
Obviously, there would be some major security concerns, but both parties enter an official agreement, it shouldn't be too much of a problem.
The company would allow you to indicate where you would like to go, casting a wider net would obviously increase your chances of finding a match, then they would look for someone that matches your requirements that also wants to visit your country and you would simply do a switch.
Alternatively, people with extra room in their houses might offer free accommodation, in exchange for receiving the same when they decide to travel.
I've searched for programs like these, but all I've been able to find has been educational programs or immersion programs like Lingoo where the client is hosted by a family, but nothing that simply provides you with a place to stay free of charge.
Not only would this provide participants with free accommodation but it is also likely to be more comfortable than hotels or backpackers, it will probably also allow participants to experience their destinations from the perspective of a local, rather than the overcommercialized tourist hotspots that one would normally travel to. It could be a great way to really experience the culture and perhaps even make friends with the person or family you are switching with.
I even thought that people might allow their vehicles to be used, which would cut down another major expense, but there might be some insurance issues with that idea and it would be difficult to keep fair, as one person might travel far while the other stays in a relatively small area.